Automatic methods for 3D motion trajectories gap filling: Custom-based Kalman vs. BiLSTM

Modern data analysis increasingly relies on time series data across diverse domains, such as biomechanics, medicine, sports, and computer animation. A special case of this data type is generated by optical motion capture systems, enabling precise spatiotemporal tracking of anatomical marker positions. However, during dynamic, fast-moving recordings, some markers may not be registered properly, mainly because they are obscured or because there are insufficient cameras. While continuous trajectories provide the basis for human movement analysis, their utility is heavily dependent on the accurate registration of all measurement points. The post-processing of motion capture data is highly time-consuming; thus, selecting an appropriate, highly reliable gap-filling method is extremely important for subsequent data analysis. In this study, we propose a novel, custom-designed Kalman filter for gap-filling dance motion-capture trajectories. This method integrates the three-dimensional positions, velocities, and accelerations of markers. The proposed method is compared with the basic Kalman filter and a bidirectional Long Short-Term Memory (BiLSTM) model, which is highly effective for imputing sequential data. Given these dual paradigms, this study aims to compare the classical mathematical model with the modern machine learning approach for reconstructing motion capture data, evaluating their respective effectiveness across varying spatial and temporal characteristics of missing data. Several examinations, based on the number of missing markers (from 2 to 14) in the given marker's neighbour group across various frame numbers (from 100 to 500), were performed. The BiLSTM model achieved lower RMSE values than the custom Kalman-based filter across almost all scenarios and was highly stable with a small number of missing markers. However, the accuracy of both methods deteriorated as the number of missing markers increased, indicating a significant impact of the spatial distribution of missing data on reconstruction quality.